Manipulating interlayer magnetic orders of 2D magnets by stacking rotation

Chromium triiodide (CrI₃), a two-dimensional (2D) van der Waals (vdW) magnet, exhibits complex magnetism depending on the number of layers and interlayer stacking patterns. Within each layer spins are ferromagnetically coupled with strong out-of-plane anisotropy, but between layers the magnetic orders can be manipulated between ferromagnetic (FM) and antiferromagnetic (AFM) by numerous ways due to the relatively weak interlayer coupling. In this talk, we considered three energetically stable stacking patterns R3, C2/m and AA in bilayer CrI₃, and the reversed counterparts R3-r, C2/m-r and AA-r through rotating one layer by with respect to the other layer. Our first-principles calculations suggest that the interlayer magnetic ground state can be switched from AFM to FM (or FM to AFM) by reversing the stacking pattern, corroborating prior experimental results in bilayer CrBr₃. Detailed microscopic analysis was carried out by magnetic force theory calculations on C2/m stacking which favors AFM and C2/m-r stacking which favors FM. The interlayer magnetic interactions and the origin of the magnetic order change were revealed through specific orbital analysis. Our work demonstrates that stacking rotation, like stacking translation, allows us to control and manipulate the interlayer magnetism of CrI₃ and possibly other 2D magnetic materials as well.